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--- en:materialdaten:rheologische_materialdaten [2024/10/17 17:15] – [Pressure shift factor β] neelest
+++ en:materialdaten:rheologische_materialdaten [2025/05/15 15:49] (aktuell) – [Pressure shift factor β] cschall
@@ Zeile 1: / Zeile 1: @@
 ======Rheological material data======
+===== Material data - Rheology =====
+The rheological data of the material is entered in the ‘Rheology’ tab:
+  * **Pressure shift factor beta**, this input is optional. Without an input value, the pressure dependence of the viscosity is neglected.
+  * **Reference temperature T_B**, the values entered in the viscosity law are valid for this temperature.
+  * **Temperature law**, the temperature dependence of the viscosity can be modelled here. The temperature shift is calculated using //PAM//. The following modelling options are available
+    * **WLF (Tb, Ts)**: Temperature shift by specifying the standard temperature T_S
+    * **WLF (C1, C2)**: Temperature shift due to the constants C1 and C2
+    * **Arrhenius**: Temperature shift due to activation energy E
+  * **Viscosity law**, the equation for describing the viscosity can be selected here. The following models are available:
+    * **Carreau**: Input of the 3 parameters a, b and c
+    * **Power law**: Input of the parameters K and n
+  * **Wall slipping**: If the checkbox is selected, the critical shear stress at 2 temperatures must be entered. See [[en:berechnungen:wandgleitende_materialien|calculation of wall sliding]]
 {{ :materialdaten:rex171_mat_en_004.png?nolink |}}
@@ Zeile 16: / Zeile 30: @@
 with shear stress $τ$, the viscosity $η$ and the shear rate $\dotγ$.
-This law states that the shear stress and the shear rate are proportional to each
+This law states that there is proportionality between the shear stress and the shear rate, whereby the proportionality factor is the viscosity. This flow behaviour only occurs in polymer liquids or melts at very low shear rates and possibly at very high ones. Deviations are expressed in the so-called pseudoplasticity (shear thinning), dilatancy or the presence of a yield point.
-other, with viscosity being the proportionality factor. In the case of polymeric fluids
-respectively melts this flow behavior occurs at a very low shear rate and occasionally
-with very high ones. Deviations are manifested in so-called structural viscosity,
-dilatancy or the presence of a flow limit.
-The flow behavior of polymer melts is characterised in the shear rate ranges that
+{{ :materialdaten:abb_stoffverhalten_en.svg?nolink&600 |}}
-exist in practice by structural viscosity. This describes a flow behavior which deviates
-from that of Newtonian fluids, where the viscosity is no longer constant but highly
-dependent on the shear rate.
-{{ :materialdaten:abb_stoffverhalten_en.svg?700 |}}
+The flow behavior of polymer melts in practically relevant shear rate ranges is characterized by so-called pseudoplasticity (shear thinning). This describes a deviation from Newtonian fluid behavior, where the viscosity is no longer constant but decreases with increasing shear rate.
-The following illustration shows the basic profile of the viscosity against the shear rate. Where the
+The following figure shows the basic viscosity curve as a function of the shear rate.
-shear rate range is not too large it is possible to describe this behavior through the
-empirically established power flow law according OSTWALD und DE WAELE:
-\[τ=K\cdot\dotγ^n\]
+{{ :materialdaten:abb_viskositaetsverlauf_en.svg?nolink&600 |}}
-$n$ is the exponent of the flow lay and $K$ is the flow lay coefficient.
+For shear rate ranges that are not too large, this behaviour can be described by the empirically found power flow law according to OSTWALD and DE WAELE:
-{{ :materialdaten:abb_viskositaetsverlauf_en.svg?700 |}}
+$$τ=K\cdot\dotγ^n$$
+respectively
+$$\eta=a_T \cdot K \cdot \gamma^{n-1}$$
-With the simple setup of this law nearly all flow problems, which are ascertainable for
+where $n$ is the exponent of the flow law and $K$ is the consistency factor.
-Newtonian fluids, can be treated analytically. In the double logarithmic depiction there
-is also for the power law model a straight line. As shown in the next figure, each curve
-segment has to be calculated with the corresponding flow exponent $n$. The
-consistency factor $K$ is described by:
-\[K = K_{0T}\cdot e^{-β(T-T_0)}\]
+Due to the simple structure of this approach, almost all flow problems can be treated analytically. In double logarithmic representation, a straight line results for the power law. For the Newtonian range, this results in $n=1$ and $K=\eta_0$. In the pseudoplastic range, the viscosity curve in small ranges can also be approximated by the power law. This results in a shear rate-dependent $n<1$.
-The constant $K_{0T}$ corresponds to the viscosity at the shear rate and the reference
+{{ :materialdaten:abb_potenz_naeherung_en.svg?nolink&600 |}}
-temperature $T_0=0°C$; the temperature dependence of the viscosity is described.
-{{ :materialdaten:abb_potenz_naeherung_en.svg?700 |}}
+The CARREAU approach offers a better description over wide ranges of the viscosity function, especially for materials with a pronounced transition from the Newtonian to the pseudoplastic range:
-A better description of further areas of the viscosity function is offered by the
+\[η = \frac {A \cdot a_T} {(1+a_T \cdot B \cdot \dotγ)^C}\]
-CARREAU-law, especially with materials which show a pronounced transition from
-the Newtonian to the low viscosity area:
-\[η = \frac {Aa_T} {(1+a_TB\dotγ)^C}\]
+Where $A$ is the zero-shear viscosity, $B$ is the reciprocal transition shear rate and $C (= 1-n)$ is the gradient.
-Here, $A$ is the zero viscosity, $B$ the reciprocal transition shear rate and $C (= 1-n)$ the
+{{ :materialdaten:abb_carreau_en.svg?nolink&600 |}}
-pitch.
-{{ :materialdaten:abb_carreau_en.svg?700 |}}
-==== Temperature shift factor α ====
-The temperature dependence is considered by the temperature shift factor aT which
+==== Temperature shift factor a${}_T$ ====
-can be determined from the WLF-relation:
-Carreau-WLF ($T_B$, $T_S$):
+The temperature dependence is taken into account by the temperature shift factor $a_T$, which can be described in three different ways
-\[lg(a_T) = \frac {C_1\cdot(T_B-T_S)} {C_2+(T_B-T_S)} - \frac {C_1\cdot(T-T_S)} {C_2+(T-T_S)}\]
+===Carreau-WLF (T_B, T_S)===
-$T_B$, $T_S$ are given, $C_1 = 8,86$, $C_2 = 101,6$
+\[log(a_T) = \frac {C_1\cdot(T_B-T_S)} {C_2+(T_B-T_S)} - \frac {C_1\cdot(T-T_S)} {C_2+(T-T_S)}\]
-o r
+$T_B$, $T_S$ must be provided, $C_1 = 8,86$, $C_2 = 101,6$
-Carreau-WLF ($C_1$, $C_2$):
+with: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature
+=== Carreau-WLF (C1, C2) ===
 \[ln(a_T) = - \frac {C_1 \cdot (T-T_B)} {C_2+(T-T_B)}\]
-$C_1$, $C_2$, $T_B$ are given
+$C_1$, $C_2$, $T_B$ must be provided
-**with**: $T_B$ = reference temperature, $T_S$ = standard temperature, $T$ = current temperature
+**with**: $T_B$ = reference temperature, $T$ = current temperature
-Carreau-Arrhenius ($E$, $T_B$):
+=== Carreau-Arrhenius (E, T_B) ===
-\[K = K_{0T}exp[\frac{\Delta E}{R} (\frac{1}{T}-\frac{1}{T_0})]\]
+$$ln(a_T)=\frac{E}{R} (\frac{1}{T}-\frac{1}{T_B}) $$
-**with**: $E$ = activating energy, $R$ = gas constant, $K_{0T}$ = physical size at the temperature $T_0$, $T_0$ = reference temperature
+**with**: $E$ = activating energy, $R$ = gas constant, $T_B$ = reference temperature (in kelvin), $T$ = current temperature (in kelvin)
-With the Carreau-law the polymer specific material behavior can be described over
-large shear rate and temperature areas.
 ==== Pressure shift factor β ====
-The pressure shift factor beta considers the pressure’s influence on the viscosity. The value refers to an average material specific temperature from PAM
+The pressure shift factor beta takes into account the influence of the pressure on the viscosity. By default, the value refers to a reference pressure of 100 bar. The pressure shift $a_p$ is included in the viscosity calculation in the same way as the temperature shift factor $a_T$. $a_p$ is calculated as follows:
-and to a reference pressure of 100 bar. The pressure dependent viscosity is
-calculated with the following equation.
-\[y(p) = (p_0)\cdot e^{β(p-p_0)}\]
+$$ a_p = exp(\beta \cdot (p-p_B))$$
-{{ :materialdaten:abb_viskositaet_druckabhaengig_en.svg?700 |}}
+with the pressure shift factor $\beta$, the pressure $p$ and the reference pressure $p_B$.
+{{ :materialdaten:abb_viskositaet_druckabhaengig_en.svg?nolink&600 |}}
 The value beta can be imported directly from PAM or entered manually. If 0 is
 entered as the value for beta, the viscosity is calculated without considering the
 pressure.
-As the law can only be used analytically to a limited extent, from this function the
-corresponding coefficients of the power law model are calculated internally for the
-occurring shear rates and temperatures. You can choose between three different
-laws in the input mask **Rheology**. All of them describe the rheological behavior of
-polymer melts. The difference of the laws is their description of the temperature shift
-function. This distinction has been introduced to guarantee an easy input despite different sources of the data (CAMPUS, BAYMAT, VISCOSITY). If the Carreau-WLF
-data is taken for example from the BASF database VISCOSITY, the setting Carreau-WLF ($C_1$, $C_2$) has to be chosen. If you want to calculate with a material from BAYER,
-the data can be taken from the BAYMAT file and entered with the help of the setting
-Carreau-WLF ($T_B$, $T_S$). Both constants $C_1$ and $C_2$ are here internally set to 8.86 or
-rather to 101.6 and cannot be edited.
-If you want to calculate a wall-slipping material with **REX/PSI**, you have to
-characterize the flow law with the help of the Carreau or the Arrhenius parameter. In
-addition you have to enter two pairs of variates, consisting of a test temperature and
-the critical wall shear stress determined at this test temperature.
-Additionally, with the material parameter $k_{mat}$ the increase of the dimensionless
-sliding speed $V_{sl}^*$ in dependence of the dimensionless shear stress $τ^*$ can be
-described. The determination of the necessary material data, like the sliding speed
-$v_{sl}$ in dependence of the wall shear stress $τ$, occurs during the viscosity
-measurement (e.g. with a high pressure capillary rheometer).
-At measuring the pressure in dependence of the volume flow, with wall-slipping melts
-discontinuities occur in the double-logarithmic diagram as opposed to wall-adhering
-melts.
-{{ :materialdaten:abb_krit_wandschubspannung_en.svg?700 |}}
-From the critical pressure $Δp_{krit}$ at which this discontinuity occurs, with the following
-formula the critical wall shear stress $τ_{krit}$ can be calculated for rectangular
-capillaries:
-\[τ_{krit} = \frac{\Delta p_{krit}}{2} \frac{h}{l}\]
-These critical shear stresses can be indicated approximately as straight line
-equations in dependence of temperature. Thus, you have to enter two pairs of variates in REX/PSI for the critical shear stresses and the temperature belonging to it.
 ===Further topics===
   * [[en:materialdaten:datenbankanbindung_an_pam|]]
   * [[en:materialdaten:allgemeineangaben|]]
-  * [[en:materialdaten:rheologische_materialdaten|]]
   * [[en:materialdaten:thermodynamische_daten|]]
   * [[en:materialdaten:dichtedaten_bzw._spezifisches_volumen|]]
+  * [[en:materialdaten:rheologische_materialdaten|]]
+  * [[en:materialdaten:technologische_daten|]]
   * [[en:materialdaten:tribologische_daten|]]
-  * [[en:materialdaten:technologische_daten|]]
+  * [[en:materialdaten:zusatzstoffe|]]
   * [[en:materialdaten:molekulargewicht|]]
   * [[en:materialdaten:faserabbau|]]
   * [[en:materialdaten:eingabe_von_mischungen|]]
-  * [[en:materialdaten:polymer-polymer_mischung|]]
-  * [[en:materialdaten:gefuelltes_polymer|]]